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The 9th Term of an A.P. is Equal to 6 Times Its Second Term. If Its 5th Term is 22, Find the A.P. - Mathematics

Sum

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

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Solution

Let a be the first term and d be the common difference.

We know that, nth term = an a + (n − 1)d

According to the question,

a9 = 6a2
⇒ a + (9 − 1)d =  6(a + (2 − 1)d)
⇒ a + 8d =  6a + 6d
⇒ 8d − 6=  6a − a
⇒ 2= 5a
⇒ a = \[\frac{2}{5}\]d   .... (1)
Also, a5 = 22
⇒ a + (5 − 1)d = 22
⇒ a + 4d = 22   ....(2)
On substituting the values of (1) in (2), we get \[\frac{2}{5}\]+ 4d = 22
⇒ 2+ 20= 22 × 5
⇒ 22= 110
⇒ = 5
⇒ a =\[\frac{2}{5} \times 5\]    [From (1)]
⇒ a = 2

Thus, the A.P. is 2, 7, 12, 17, .... .

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 40 | Page 26
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